I always assumed where it came to TOS a couple things.
First Kirk says 'there are only 12 others LIKE her'; the implication being the fleet even then consisted of a lot more ships, but probably smaller and less capable than Constitution Class, which would have been a 'ship of the line' so to speak.
This seems almost a hard requirement given how many assets they visit, space stations, research out posts, listening stations, etc.. It does not seem like independent commercial interests would have built out all that, especially in the context of the 'post scarcity' world even TOS mostly operates in. I mean who dreams of hanging out on some small space station shuffling Quadrotriticale between transport ships? At the very least someone has to tell you 'it is noble work' or provide so motivation, so there has to be a command element to the economy. I digress, the critical point here the existence of these transports implies there are lots of other space faring vessels even in this early cannon. By extension it would make sense than Star Fleet would not be having captial ships returning to base for supplies etc, but probably at the least has tenders and things of the like in it.
As far as encountering new disasters again forward exploration is the Enterprises role, they are largely operating in least explored regions of known space furthest from support, they are seeking out 'new' things.
Presumably the other twelve Star Ships are also experiencing similarity wild events; we see this in the Planet Killer, where Enterprise is the second the party after Constellation.
Finally yes they do publish the results. In TNG's "The Naked Now" the have a complete record of the events of the "The Naked Time" in the in the ships database. So at least within Star Fleet the pretty much everything another ship encounters is available and searchable to you including the logs of the ships command crew, at least if you have clearance.
